Koorde is a new distributed hash table (DHT) based on Chord [15] and the de Bruijn graphs [2]. While inheriting the simplicity of Chord, Koorde meets various lower bounds, such as O(log n) hops per lookup request with only 2 neighbors per node (where n is the number of nodes in the DHT), and O(log n/ log log n) hops per lookup request with O(log n) neighbors per node.

Abstract-The computational issues related to information in-tegration in multisensor systems and distributed sensor networks has become an active area of research. From a computational viewpoint, the efficient extraction of information from noisy and faulty signals emanating from many sensors requires the solution of problems related a) to the architecture and fault tolerance of the distributed sensor network, b) to the proper synchronization of sensor signals, and c) to the integration of information to keep the communication and the centralized processing require-ments small. In this paper, we propose a versatile architecture for a distributed sensor network which consists of a multilevel network with the nodes (processing elementlsensor pairs) at each level interconnected as a deBruijn network. We show that this multilevel network has reasonable fault tolerance, admits simple and decentralized routing, and offers easy extensibility. We model information from sensors as real valued intervals and derive an interesting property related to information integration in the presence of faults. Using this property, the search for a fault is narrowed down to two potentially faulty sensors or communication links. In a distributed environment, information has to be integrated from “temporally close ” signals in the presence of imperfect clocks in a distributed environment. We apply the results of past research in this area to state various relationships between the clocks of the processing elements in the network for proper information integration. Index Terms- Abstract estimate, clock synchronization, dis-tributed sensor networks, deBruijn networks, fault tolerance, information integration. I.

A connected hypercube with faulty links and/or nodes is called an injured hypercube. To enable any non-faulty node to communicate with any other non-faulty node in an injured hypcrcube, the information on component failures has to be made available to non-faulty nodes so as to route messages around the faulty components. We propose first a distributed adaptive fault-tolerant routing scheme for an injured hypercube in which each node is required to know only the condition of its own links. Despite its simplicity, this scheme is shown to be capable of routing messages successfully in an injured hypercube as long as the number of faulty components is less than n. Moreover, it is proved that this scheme routes messages via shortest paths with a rather high probability and the expected length of a resulting path is very close to that of a shortest path. Since the assumption that the number of faulty components is less than n in an n-dimensional hypercube might limit the usefulness of the above scheme, we also introduce a routing scheme based on depth-first search which works in the presence of an arbitrary number of faulty components. Due to the insufficient information on faulty components, however, the paths chosen by the above scheme may not always be the shortest. To guarantee all messages to be routed via shortest paths, we propose to equip every node with more information than that on its own links. The effects of this additional information on routing efficiency are analyzed, and the additional information to be kept at each node for the shortest path routing is determined. Several examples and remarks are also given to illustrate bur results. Index Terms: Injured and regular hypercubes, distributed adaptive fault-tolerant routing, dcpthfirst search, looping effects, network delay tables, failure information.

The paper is a survey of networking solutions that have been proposed for high-speed packet-switched applications. Using these solutions as examples, we identify the specific problems resulting from very high transmission rates and explain how these problems influence the design of high-speed networks and protocols. We conclude that the solutions based on deflection routing are the most promising ones and we suggest a number of directions for their evolution. 1 Introduction Not so long ago, computer networks with high transmission rates (e.g. several Mb/s) were naturally confined to local domains. Although such (and higher) transmission rates were available in telephony on long distances, they were used on a point-to-point basis. Concepts of highly-connected fast networks spanning geographical areas larger than the acreage typically covered by a single institution are relatively new and, besides the emerging atm technology, there are no standard commercially available solutions that c...

Abstract — Fault-tolerant systems aim at providing continuous operation in the presence of faults. Multicomputers rely on an interconnection network between processors to support the message-passing mechanism. Therefore, the reliability of the interconnection network is very important for the reliability of the whole system. This paper analyzes the effective redundancy available in a wormhole network by combining connectivity and deadlock freedom. Redundancy is defined at the channel level. We propose a sufficient condition for channel redundancy, also computing the set of redundant channels. The redundancy level of the network is also defined, proposing a theorem that supplies its value. This theory is developed on top of our necessary and sufficient condition for deadlock-free adaptive routing. The new theory also considers the failure of physical channels when virtual channels are used. Finally, we propose a methodology for the design of fault-tolerant routing algorithms, showing its application to n-dimensional meshes. Index Terms—Adaptive routing, channel redundancy, fault-tolerant routing, interconnection networks, network redundancy, wormhole switching. 1

this paper, we study the routing problem for the undirected binary de Bruijn interconnection network. Researchers have never proposed a shortest path routing algorithm on the undirected binary de Bruijn network. We first propose a shortest path routing algorithm, whose time complexity in the binary de Bruijn network of 2 m m m nodes is O O O(m m m ). Then, based on our shortest path routing algorithm, we propose two fault-tolerant routing schemes. It is assumed that at most one node fails in the network. In our schemes, two node-disjoint paths are found. Our first fault-tolerant routing algorithm guarantees that one of the two paths is the shortest path, and the other is of length at most m m m + log 2 m m m + 4. Our second algorithm can find two node-disjoint paths with lengths at most m m m and m m m + 4, respectively, if the shortest path is not required in the fault-tolerant routing. 2000 John Wiley & Sons, Inc

De Bruijn graphs, both directed and undirected, have received considerable attention as architecture for interconnection networks. In this paper, we focus on undirected de Bruijn networks of radix d and dimension n, denoted by UB(d;n). We first discuss the shortest-path routing problem. We present properties of the shortest paths between any two vertices of UB(d;n) and propose two shortest-path routing algorithms, one of which has linear time complexity. Secondly, we study the transmitting problem. We establish a lower bound for the optimal transmitting time which implies in particular that the optimal transmitting problem is trivial for UB(d;n) when d 5. We present a transmitting scheme on undirected binary de Bruijn networks UB(2;n) with transmitting time n \Gamma 1 for n 5, and conjecture that the optimal transmitting time is n \Gamma 1 for UB(2;n), and n for UB(3;n) and UB(4;n). Index Terms: Interconnection networks, de Bruijn networks, shortest paths, string matching, prefix ...

We show in this paper that de Bruijn networks, despite providing efficient search while using constant routing table size, as well as simplicity of the understanding and implementation of such networks, are unsuitable where key distribution will be uneven, a realistic scenario for most practical applications. In presence of arbitrarily skewed data distribution, it has only recently been shown that some traditional P2P overlay networks with non-constant (typically logarithmic) instead of constant routing table size can meet conflicting objectives of storage load balancing as well as search efficiency. So this paper, while showing that de Bruijn networks fail to meet these dual objectives, opens up a more general problem for the research community as to whether P2P systems with constant routing table can at all achieve the conflicting objectives of retaining search efficiency as well as storage load balancing, while preserving key ordering (which leads to uneven key distribution).

In this paper, we aim to embed a longest path between every two vertices of a star graph with at most n-3 random edge faults, where n is the dimension of the star graph. Since the star graph is regular of degree n-1, n-3 (edge faults) is maximum in the worst case. We show that when n≥6 and there are n-3 edge faults, the star graph can embed a longest path between every two vertices, exclusive of two exceptions in which there are at most two vertices missing from the longest path. The probabilities of the two exceptions are analyzed. When n≥6 and there are n-4 edge faults, the star graph can embed a longest path between every two vertices. The situation of n<6 is also discussed.

Making high-bandwidth Internet access pervasively available to a large worldwide audience is a difficult challenge, especially in many developing regions. As we wait for the uncertain takeoff of technologies that promise to improve the situation, we propose to explore an approach that is potentially more easily realizable: the use of digital storage media transported by the postal system as a general digital communication mechanism. We shall call such a system a Postmanet. Compared to more conventional wide-area connectivity options, the Postmanet has several important advantages, including wide global reach, great bandwidth potential, low cost, and ease of incremental adoption. While the idea of sending digital content via the postal system is not a new one, none of the existing attempts have turned the postal system into a generic and transparent communication channel that not only can cater to a wide array of applications, but also effectively manage the many idiosyncrasies associated with using the postal system. In the proposed Postmanet, we see two recurring themes at many different levels of the system. One is the simultaneous exploitation of the Internet and the postal system so we can combine their latency and bandwidth advantages. The other is the exploitation of the abundant capacity and bandwidth of the Postmanet to improve